1. Field
The present disclosure relates to the field of communications, and in particular to a method for estimating frequency offset, an apparatus and a system.
2. Background
In a coherent optical communication system, there often exists frequency offset between a laser at a transmitter end and a laser at a receiver end, and this frequency offset must be estimated and compensated for when a transmitted signal is recovered at the receiver end. A commonly-used method for estimating frequency offset is to use correlation of a signal. A sequence is transmitted repeatedly at the transmitter end, and their correlation values are calculated at the receiver end. The correlation value can be calculated only when the sequence is transmitted repeatedly at least twice. And if it is repeatedly transmitted many times, multiple correlation values may be calculated and then averaged, so as to reduce influence of noises.
For the sake of simplicity, in the following description, two times of repeating is taken as an example. FIG. 1 is a schematic diagram of a signal containing two identical sequences. As shown in FIG. 1, wherein L is the length of the sequence, and s is a starting position.
A sampled signal at the receiver end may be denoted as r(i), i in parenthesis is an integer, denoting a serial number of a sampling point. And calculation of correlation may be expressed as:c=Σi=0L-1r(s+i)r*(s+i+L);
where, * denotes a conjugate, s is a starting position of the two identical time domain signal waveforms, L denotes a length of a sequence that is repeatedly transmitted. The following formula may be calculated according to an argument of the correlation value c:
      δ    ⁢                  ⁢    f    =                    arg        ⁡                  (          c          )                            2        ⁢                                  ⁢        π              ⁢                            f          s                L            .      
This estimation is referred to as decimal frequency offset estimation. As a range of the arg(⋅) calculation is [−π, π], a range of δf is [−fs/2L, fs/2L]. However, actual frequency offset may exceed such a range, and the exceeded part is referred to as integer frequency offset, which must be an integer multiple of fs/L, and total frequency offset may be expressed as:
      Δ    ⁢                  ⁢    f    =            n      ⁢                        f          s                L              +          δ      ⁢                          ⁢              f        .            
In the above formula, the frequency offset is written as a sum of two parts, the first part
  n  ⁢            f      s        L  is referred to as integer frequency offset, and the second part δf is referred to as decimal frequency offset. As the range size of δf is fs/L, seamless frequency offset estimation may be achieved only if the integer n is determined.
In an orthogonal frequency division multiplexing (OFDM) system, an existing method for estimating frequency offset is divided into two steps. In the first step, decimal frequency offset is estimated in a time domain, in which correlation of two repeated signals (specially designed OFDM symbol, or cyclic prefix contained in an OFDM signal) is often used (refer to references [1] and [2]). After the decimal frequency offset is compensated for, FFT (fast Fourier transformation) is performed on the signals, so as to obtain frequency domain signals. In the second step, integer frequency offset is estimated in a frequency domain. Some zero-padded virtual carriers are added into both sides of a spectrum of an OFDM signal, so as to achieve over-sampling, as shown in FIG. 2. In an ideal case, see FIG. 2A in detail, power of subcarriers carrying data is non-zero, and power of the virtual carriers is zero. According to positions of the virtual carriers in the spectrum, or after finding subcarriers of relatively high power, the integer frequency offset may be deducted (refer to reference [3]). However, in an actual optical transmission system, as being subjected to noises and various transmission damages, a received signal may possible have certain power at a position of a virtual carrier, as shown in FIG. 2B. And a filter in a channel will change a spectral shape of the signal, and power of subcarriers carrying data close to the positions of the virtual carriers may possibly become relatively low, with low discrimination with the virtual carriers, resulting in greatly lowering the reliability of the method. The other method is to use pilot signals added to specific subcarriers. For example, in reference [4], pilot data in specific subcarriers of several consecutive OFDM symbols are set to be identical, and positions of the pilot subcarriers in a frequency domain may be determined according to this feature, thereby determining the integer frequency offset.
For a single-carrier system, the frequency offset estimation may be performed before equalization (refer to reference [5]). This method is fast in speed, needs no equalization, but is low in precision. The frequency offset estimation may also be performed after equalization (refer to reference [6]), but this method needs relatively long time of iterative convergence to obtain a result of frequency offset estimation, and the signals need to be subjected to equalization first.